The resonance frequencies of a woodwind instrument can be calculated b
y modelling it as a lattice of series and parallel tube pieces. For gr
eater accuracy, corrections due to local changes in compliance and ine
rtance by the presence of holes must be taken into account. The compli
ance change due to a closed hole is determined by its volume. The iner
tance change is dependent on both hole volume and shape. A quick estim
ate of the inertance is obtained when approximating the flow as strati
fied and summing the results of the parallel layers using values from
accurately obtainable two-dimensional results. This solution has a sys
tematic error. A correct solution is obtained by a finite difference m
ethod, but its accuracy is limited by the number of elements which can
be handled by a computer. Results of both approaches are compared. Fo
r a closed cylindrical hole, the Volume contributing to the (negative)
inertance change is found to be approximately 28% of the hole radius
times its area. The inner end correction for an open hole is found to
vary between 82% and 16% of the hole radius when the ratio of hole and
tube radii varies between zero and unity.